The present invention relates to a method and apparatus for the quantification of muscle tone. More particularly, the present invention relates to a method and device that utilize non-sinusoidal perturbations to quantify muscle tone. The device is, and method are particularly useful in quantifying muscle tone in a spastic patient.
Individual skeletal muscle cells are mechanically and anatomically arranged in parallel. The total force produced by a muscle is equal to the sum of the forces generated by its constituent cells. In the normal subject, muscles that comprise the wrist flexors and extensors are normally relaxed and are usually recruited to generate force and movement.
Lower motor neuron paralysis occurs when muscles are deprived of their immediate nerve supply from the spinal cord. This occurs when a nerve between the spinal cord and a muscle is cut or when cell bodies of the ventral horn are destroyed as in poliomyelitis. Muscles become soft and atrophic, and reflex response to sensory stimuli is lost. Most nerve disorders that affect limb function are due to upper motor neuron paralysis, wherein damage is present somewhere in the corticospinal tract that originates in the brain and travels through the spinal cord.
Spasticity is defined as abnormal involuntary contraction of a muscle or group of muscles due to a rate-dependent reflex mechanism. The spindle elicits the reflex response upon deformation. To a certain extent, these reflexes are normal and important. In normal operation, these reflexes are suppressed to a certain extent to allow flexibility and motion of joints. In spasticity however, there is a disruption in the normal behavior of the stretch reflex that causes muscles, particularly the flexors, to be extremely resistive to passive stretch (i.e. high in tone). As a result, motor control is severely impaired and stiffness or tightness of the muscles may interfere with gait, movement, and speech. Spasticity is usually found in people with some sort of upper motor neuron paralysis, such as those with cerebral palsy, traumatic brain injury, spinal cord injury and stroke patients.
Common symptoms of spasticity may include hypertonicity (increased muscle tone), clonus (a series of rapid muscle contractions), exaggerated deep tendon reflexes, muscle spasms, scissoring (involuntary crossing of the legs) and fixed joints. The degree of spasticity varies from mild muscle stiffness to severe, painful, and uncontrollable muscle spasms. The condition can interfere with rehabilitation in patients with certain disorders, and often interferes with daily activities.
Many forms of intervention are available to reduce muscle tone in spasticity. Biochemical pharmaceuticals such as Botox (Botulinum Toxin Type A), Intrethecal Baclofen, and Zanaflex (tizanidine) may be used as a biochemical form of intervention. (See R. W. Armstrong, P. Steinbok, D. D. Cochrane, et al. Intrathecally administered baclofen for treatment of children with spasticity of cerebral origin. J Neurosurg; 87(3):409-414, Sep 1997; J. V. Basmajian, K. Shankardass, D. Russel: Ketazolam Once Daily for Spasticity: Double-Blind Cross-Over Study. Arch. Phys. Med. Rehabil. Vol. 67, pp556-557, 1986; P. J. Delwaide: Electrophysiological Analysis of the Mode of Action of Muscle Relaxants in Spasticity. Annals of Neurology, Vol. 17, No. 1, January 1985, pp 90-950). These chemicals are used either to destroy nerve endings at the neuromuscular junction, or they are used as blocking agents which depress neuromuscular transmission by competing with acetylcholine for receptors, thus suppressing nerve conduction. In severe cases, microsurgery is also an option, where incisions are made in the brainstem or anywhere in the stretch reflex pathway. The safest form of intervention is physical therapy, such as training, stretching exercises and casting. (J. C. Otis, L. Root, M. A. Kroll: Measurement of Plantar Flexor Spasticity During Treatment with Tone-Reducing Casts. Journal of Pediatric Orthopedics 5:682-686, 1985).
Tone is defined as the degree of resistance to stretch from an external source. An assessment of tone is important in evaluating the degree of spasticity that a patient has. This assessment is imperative for the clinician to decide what form of intervention to take and to what degree. Further, continued assessment throughout intervention is important to assess the effectiveness of the intervention. For example, if the Botox dosage administered is too low, it may have little or no effect in reducing a patient""s spasticity. Conversely, if the dosage is too high, then the patient may lose the ability to control his or her limb, as blocking too many neuromuscular junctions at the muscle site may prevent the central nervous system from having any control over the muscle. An assessment of tone before and after intervention is also important as it can demonstrate the effectiveness of the treatment.
Probably the most widely accepted clinical test for the evaluation of tone in spasticity is the Ashworth scale shown below in Table 1.
The clinician moves the subject""s limbs about the joints and then assigns a grade based on a xe2x80x9ctouchy feelyxe2x80x9d assessment of how much resistance the clinician feels. One can easily see the problem here. Since the test is a qualitative one, different clinicians may assign different grades to the same test. Even the same clinician""s evaluation may change due to lack of consistency or depending on whether he or she is optimistic or pessimistic at the time of the test. The clinician may also be biased and may, for example, assign a better grade if he or she has knowledge of interventions being performed on the patient. Even putting all these issues aside, it is difficult to get an absolute measure of tone using the Ashworth scale. As stated in a review article xe2x80x9cThe quantification of spasticity has been a difficult and challenging problem, and has been based primarily on highly observer-dependent measurements. The lack of effective measurement techniques has been restrictive, since quantification is necessary to evaluate various modes of treatment.xe2x80x9d (R. T. Katz, W. Rymer: Spastic hypertonia; mechanisms and measurement. Archives of Physical Medicine and Rehabilitation. 1989; 70:144-145).
In attempt to quantify muscle tone, some have used Electromyography (EMG) information. (See P. J. Delwaide: Electrophysiological Analysis of the Mode of Action of Muscle Relaxants in Spasticity. Annals of Neurology, Vol. 17, No. 1, January 1985, pp 90-95; A. Eisen: Electromyography in Disorders of Muscle Tone. Le Journal Canadien des Sciences Neurologiques, Vol. 14, No. 3. August 1987, pp 501-505; W. G. Tatton, P. Bawa, I. C. Bruce, R. G. Lee: Long Loop Reflexes in Monkeys: An Interpretative Base for Human Reflexes. Cerebral Motor Control in Man.: Long Loop Mechanisms. Prog. clin. Neurophysiol., vol 4, Ed. J. E. Desmedt, pp 229-245, Krager Basel, 1978). EMG electrodes measure and amplify actual action potentials sent to the muscles. Thus, they can monitor the stretch reflex in action and the active force of muscles can be monitored.
However, the total force of muscles is a combination of both the active and passive forces. Active tension is due to muscle stimulation and contraction due to crossbridge cycling. Independent of muscle stimulation and crossbridge cycling, muscles also experience passive tension. Like all materials, muscles experience a passive tension when they are stretched beyond their resting lengths. This is due to the inherent mechanical properties of connective tissue in the muscles, such as elastin. The total force of the muscle is the sum of the active and passive tensions, as shown in FIG. 1. If muscles were de-innervated, then there would be no active force and the total force would just be the passive force.
EMG electrodes cannot monitor passive tension. Thus, the EMG signal is correlated to the active force exhibited by the muscle but not the total force. The most common definition of spasticity is xe2x80x9ca motor disorder characterized by a velocity-dependent increase in muscle tonic stretch reflexes (muscle tone) with exaggerated tendon jerks, resulting from hyperexcitability of the stretch reflex, as one component of the upper motor neuron syndrome.xe2x80x9d (J. W. Lance: Symposium Synopsis: Disordered Motor Control, R. G. Feldman, R. R. Young, W. P. Koella, Chicago, Year Book Pulishers, 1980, pp. 485-494). However, it has also been proposed that an increase in tone is largely caused by changes in the intrinsic mechanical properties of the muscle tissue that causes an increase in the passive stiffness of the muscle. This contribution of muscle tone is independent of the stretch reflex and is not encapsulated in the EMG signal. Still further, EMG signals are extremely noisy, particularly if surface electrodes are used. EMG signals measured with surface electrodes can also be influenced by hair, oil, or lotions, and dead skin, thereby i yielding erroneous results. Though the amplitude of the EMG signal is correlated with the active force produced by the muscle, it is extremely difficult to find the proper transformation between the two quantities. This relationship differs from person to person due to physiological differences. It is also sensitive to changes in location of the electrode within the same subject. Thus, the use of an EMG machine is not a good option for quantifying muscle tone, but, rather, is more useful for monitoring the timing of reflex responses.
Still other tests, such as the pendulum test, measure the range of motion and rate of change of motion of the joint in response to a tendon jerk test. Though such tests may give an indication of tone, the trajectory of a joint does not give a full picture of muscle tone.
Tone describes the relationship of torque produced by the muscles in response to an induced trajectory perturbation, or the resulting trajectory given a torque perturbation. Either way, the relationship between torque and trajectory can be described using a mathematical model where parameters quantify tone in terms of the viscoelastic properties of the muscles. However, it is difficult to quantify these parameters. Unlike heart rate or blood pressure, which are inherently physical quantities that can be measured, tone describes a relationship between torque and displacement, as well as the first derivative of angular displacement or velocity of the joint based on the viscoelastic properties of the muscles. Also, inertia of the limb has influence on the torque, which needs to be properly isolated when determining the viscoelastic properties of the muscles acting on a joint.
In the past, simple DC motors have been used to oscillate an appendage about its joint while measuring the torque response due to the external perturbation. The response of appendage movements about the joint of rotation can be explained in terms of elastic and viscous parameters. These parameters are dependent upon the passive mechanical properties of muscles and the active stretch reflex response, which has some inherent delay. A certain amount of torque is required to move the appendage and to move the parts of the apparatus, as every mass has a rotational inertia. Thus, the torque response measured can be written as equation 1 shown below:                                                         τ              s                        ⁡                          (              t              )                                =                                                    K                H                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢                              θ                ⁡                                  (                  t                  )                                                      +                                          B                H                            ⁢                                                θ                  .                                ⁡                                  (                  t                  )                                                      +                                          J                T                            ⁢                                                θ                  ¨                                ⁡                                  (                  t                  )                                                                    ⁢                  
                ⁢                                            τ              s                        ⁡                          (              t              )                                =                                                    K                H                            ⁡                              (                                                      θ                    ⁡                                          (                      t                      )                                                        -                                      θ                    RP                                                  )                                      +                                          B                H                            ⁢                                                θ                  .                                ⁡                                  (                  t                  )                                                      +                                          J                T                            ⁢                                                θ                  ¨                                ⁡                                  (                  t                  )                                                                    ⁢                  
                ⁢                                            τ              s                        ⁡                          (              t              )                                =                                                    K                H                            ⁢                              θ                ⁡                                  (                  t                  )                                                      +                                          B                H                            ⁢                                                θ                  .                                ⁡                                  (                  t                  )                                                      +                                          J                T                            ⁢                                                θ                  ¨                                ⁡                                  (                  t                  )                                                      -                                          K                H                            ⁢                              θ                EQ                                                    ⁢                  
                ⁢                                            τ              s                        ⁡                          (              t              )                                =                                                    K                H                            ⁢                              θ                ⁡                                  (                  t                  )                                                      +                                          B                H                            ⁢                                                θ                  .                                ⁡                                  (                  t                  )                                                      +                                          J                T                            ⁢                                                θ                  ¨                                ⁡                                  (                  t                  )                                                      +                          τ              off                                                          [Eq.  1]            
where xcfx84s is the total torque sensed by the transducer. xcfx84off is the offset torque and tells the angular position the hand prefers to be in relative to the origin or bias position. KH and BH are the angular stiffness and viscosity of the combined flexor and extensor muscle groups that act on the joint. JT is the combined inertia of oscillating appendage, JH and the rotating components of the apparatus, JA. JT=JH+JA. xcex8 is the angular displacement of the system.       θ    .    ⁢      xe2x80x83    ⁢  and  ⁢      xe2x80x83    ⁢      θ    ¨  
are the velocity and acceleration which are the first and second derivatives of displacement respectively. xcex8RP is the angular position of the resting hand.
This second order differential equation has previously been used as a model by many including Evans at al (C. M. Evans, S. J. Fellows, P. M. H. Rack, H. F. Ross and D. K. W. Walters: Response of the Normal Human Ankle Joint to Imposed Sinusoidal Movements. J. Physiol. (1983), 344, pp. 483-502), Rack et al. (P. M. H. Rack, H. F. Ross and T. I. H. Brown: Reflex Response during Sinusoidal Movements of Human Limbs. Prog. Clin. Neurophysiol., vol. 4, Ed. J. E. Desmedt, pp 216-228, 1978), Lehmann et al. (J. F. Lehmann, R. Price, B. J. DeLateur, S. Hinderer, C. Traynor: Spasticity: Quantitative Measurements as a Basis for Assessing Effectiveness of Therapeutic Intervrntion. Arch. Phys. Med. Rehabil. Vol 70. pp 6-15, 1989), Prince et al. (R. Price, K. F. Bjornson, J. F. Lehmann, J. F. McLaughlin, R. M. Hays: Quantitative Measurement of Spasticity in Children with Cerebral Palsy. Developemental Medicine and Child Neurology, 33, pp.585-595, 1991), Minders et al. (M. Meinders, R. Price, J. F. Lehmann, K. A. Questad: The Stretch Reflex Response in the Normal and Spastic Ankle: Effect of Ankle Position. Arch. Phys. Med. Rehabili. Vol 77. pp 487-491, 1996). In each case, simple sinusoidal displacements of the ankle or finger joint were used at various frequencies. The technique of measuring the frequency response to sinusoidal inputs to investigate properties of second order electromechanical systems is common and easy to do. The goal is to compute KH and BH at various frequencies of oscillation. Since the activation stretch reflex loop in the central nervous system is rate-dependent, one would expect that KH and BH vary at different perturbation speeds. Sinusouds have been chosen because they are easy to generate by means of a unidirectional rotating wheel and crank. No feedback loop is necessary. It has been argued that since sinusoidal movements are continuous and smooth, they involve no sudden impulsive movements that might synchronize a large number of sensory receptors in an artificial or unphysiological way.
However, there is a fundamental mathematical problem in isolating the inertia from the elastic stiffness of the muscles when using simple sinusoidal displacements.
In this case, the displacement, xcex8(t)=Axc2x7sin(xcfx89t), where A is the amplitude of the sinusoid in radians and xcfx89 is the frequency of the oscillation in rads/sec. The velocity,             θ      .        ⁢          (      t      )        =                    ⅆ        θ            /              ⅆ        t              =          A      ⁢              xe2x80x83            ⁢              ω        ·        cos            ⁢              xe2x80x83            ⁢              (                  ω          ⁢                      xe2x80x83                    ⁢          t                )            
and the acceleration             θ      ¨        ⁢          (      t      )        =                              ⅆ          2                ⁢        θ            /              ⅆ                  t          2                      =                  -        A            ⁢              xe2x80x83            ⁢                        ω          2                ·        sin            ⁢              xe2x80x83            ⁢                        (                      ω            ⁢                          xe2x80x83                        ⁢            t                    )                .            
Substituting these state variables into equation 1 and rearranging, we get:
xcfx84sxe2x88x92xcfx84off=KHA sin(xcfx89t)+BHAxcfx89 cos(xcfx89t)xe2x88x92JTAxcfx892 sin(xcfx89t)
xcfx84sxe2x88x92xcfx84off=(KHxe2x88x92JTxcfx892)(A sin(xcfx89t))+BHxcfx89(A cos(xcfx89t))xe2x80x83xe2x80x83[Eq. 2]
The dominant waveform of the torque response is a sinusoid of the same frequency but xcfx86 radians out of phase with the displacement wave as shown in equation 3. After data acquisition, A, M and xcfx86 are obtained by looking at the transfer functions of the displacement and torque signals in the frequency domain to obtain the magnitude and phases at the forced frequency xcfx89
xcfx84sxe2x88x92xcfx84off=M sin(xcfx89t+xcfx86) xe2x80x83xe2x80x83[Eq. 3]
From the sum formula:
xcfx84sxe2x88x92xcfx84off=M sin(xcfx86)cos(xcfx89t)+M cos(xcfx89)sin(xcfx89t) If M1=M sin(xcfx86) and M2=M cos(xcfx86)
Then:
xcfx84sxe2x88x92xcfx84off=M1 cos(xcfx89t)+M2 sin(xcfx89t) xe2x80x83xe2x80x83[Eq. 4]
Substituting equation 4 into equation 2:
M1 cos(xcfx89t)+M2 sin(xcfx89t)=(Ksxe2x88x92JTxcfx892)(A sin(xcfx89t))+BHxcfx89(A cos(xcfx89t))
Thus, the total torque measured can be isolated as a component in phase with the displacement wave and a component quadrature with the displacement wave.
M1/A=KHxe2x88x92JTxcfx892xe2x80x83xe2x80x83[Eq. 5]
and
M2/A=BHxcfx89xe2x80x83xe2x80x83[Eq. 6]
The amplitude of the in phase component contains both elastic and inertial terms. Researchers have argued that a least squares (error) fit of the in phase component and displacement amplitude with frequency squared yields a linear relationship of slope intercept form; y=mx+b, where y is M1/A, x is xcfx892, m is the slope and b is the intercept. They have assumed that the slope is the total inertial and this xe2x80x9ctotal inertiaxe2x80x9d value has been used to evaluate the stiffness by manipulating equation 5 to solve for KH at each frequency.
At first glance of equation 5, this assumption may seem correct. After all, the total inertia does remain constant. However, the assumption is false because the least squares fit yields an intercept, b, that is a single approximation of KH across all frequencies. Since the goal is to find a pair of varying stiffness and viscosity values at each frequency, this analysis is self-contradictory. This analysis forces the KH values to be trendless (uncorrelated) across frequencies whose variance depends on how well equation 5 fits to a straight line. To put it simply, there are more unknowns than equations. If N sinusoids are used, each at a different forcing frequency, we are looking for N different stiffness values and one inertia value. Thus, there are N+1 unknowns and N number of equations that resemble equation 5. With more unknowns than equations, the system is indeterminate and it is impossible to isolate the stiffness values from the inertia value when only sinusoids are used.
Another way to show this problem that prevents isolation of the stiffness and inertial values from the in phase component can be shown using least squares regression analysis. Usually, we can obtain the linear parameters of the model in equation 1 by performing a least squares regression fit on the data. Given any set of data values obtained from a given perturbation trial:             T      s        =                            "LeftBracketingBar"                                                                                          τ                    s                                    ⁡                                      (                                          t                      1                                        )                                                                                                                                            τ                    s                                    ⁡                                      (                                          t                      2                                        )                                                                                                      ⋮                                                                                                          τ                    s                                    ⁡                                      (                                          t                      n                                        )                                                                                "RightBracketingBar"                          n          xc3x97          1                    ⁢              xe2x80x83            ⁢      and            Ψ    =                  "LeftBracketingBar"                                            1                                                      θ                ⁡                                  (                                      t                    1                                    )                                                                                                      θ                  .                                ⁡                                  (                                      t                    1                                    )                                                                                                      θ                  ¨                                ⁡                                  (                                      t                    1                                    )                                                                                        1                                                      θ                ⁡                                  (                                      t                    2                                    )                                                                                                      θ                  .                                ⁡                                  (                                      t                    2                                    )                                                                                                      θ                  ¨                                ⁡                                  (                                      t                    2                                    )                                                                                        ⋮                                      ⋮                                      ⋮                                      ⋮                                                          1                                                      θ                ⁡                                  (                                      t                    n                                    )                                                                                                      θ                  .                                ⁡                                  (                                      t                    n                                    )                                                                                                      θ                  ¨                                ⁡                                  (                                      t                    n                                    )                                                                    "RightBracketingBar"                    n        xc3x97        4            
It is possible to obtain the set of four parameters,       N    ~    =            "LeftBracketingBar"                                                  τ              off                                                                          K              H                                                                          B              H                                                                          J              T                                          "RightBracketingBar"              4      xc3x97      1      
that describes the model in equation 1                                          τ            s                    ⁡                      (            t            )                          =                                            K              H                        ⁢                          θ              ⁡                              (                t                )                                              +                                    B              H                        ⁢                                          θ                .                            ⁡                              (                t                )                                              +                                    J              T                        ⁢                                          θ                ¨                            ⁡                              (                t                )                                              +                      τ            off                                              [eq.1]            
using the pseudo-inverse which minimizes the sum squared error
SE=(Ôsxe2x88x92ØÑ)T(Ôsxe2x88x92ØÑ)
Vemf=Ke
Typically, the pseudo-inverse (denoted by the function pinv in equation 7), can be used to obtain the vector of unknowns, P, as follows:
Ñ=pinv(Ø)Ôs=(ØTØ)xe2x88x921ØTÔsxe2x80x83xe2x80x83[eq. 7]
However, this can usually but not always be done because, in the case of sinusoidal perturbation at a given frequency, the acceleration waveform is always a constant multiple of the displacement waveform by the scalar quantity xe2x88x92Axcfx892 for all time. Thus the displacement values and acceleration values are linearly dependent. Since the first and third rows of xcexa8 are linearly dependent, the product of the matrices xcexa8Txcexa8 is singular or very close to singular. All singular matrices are noninvertible, thus P cannot be obtained, or the obtained values are inaccurate.
The present invention provides a method and apparatus that quantifies muscle by using non-sinusoidal perturbations. More particularly, the device and method move the upper or lower extremities of a patient in a non-sinusoidal trajectory, xcex8(t), while measuring the torque response xcfx84s(t) and utilizing Equation 1 to determine the stiffness KH, viscosity BH and inertial JT parameters.                                           τ            s                    ⁡                      (            t            )                          =                                            K              H                        ⁢                          θ              ⁡                              (                t                )                                              +                                    B              H                        ⁢                                          θ                .                            ⁡                              (                t                )                                              +                                    J              T                        ⁢                                          θ                ¨                            ⁡                              (                t                )                                              +                      τ            off                                              [Eq.  1]            
In an exemplary embodiment, as set out herein in more detail, the device and method of the present invention can be utilized to quantify the forearm muscle tone, the wrist in particular. The device is particularly useful for quantifying muscle tone in a spastic patient. However, it is to be understood that the present method and device are not limited to quantification of forearm muscle tone or to the spastic patient. Rather, the device and method are useful on both the upper and lower extremities including, for example, the ankle. Further, the method and device can be used to measure muscle tone in the non-spastic patient. For example, the method and device are useful in evaluating patients with various types of upper or lower motor neuron paralysis that affects skeletal muscles, such as patients with cerebral palsy, traumatic brain injury, spinal cord injury, stroke, or Parkinson""s Disease patients. Further, the method and device could be used in analyzing a patient""s muscle tone in line with, for example, physical therapy that the patient is undergoing to regain control of the muscles in the legs after a spinal accident.
More specifically, in accordance with an exemplary method of the present invention, the wrist is driven with an arbitrary trajectory that is neither sinusoidal nor ramp. By controlling the trajectory xcex8(t) and measuring the torque response xcfx84(t), the stiffness, viscosity, and inertial parameters in equation 1 can then be determined.
In general, the device in accordance with the present invention is an automated tone assessment device that non-invasively and properly quantifies tone. The device properly determines the muscle tone of a person""s flexors and extensors about a appendage non-invasively. The appendage is perturbed with arbitrary trajectories by virtue of a robotic design that uses a closed loop automated feedback direct drive device that tracks any arbitrary desired trajectory. The device perturbs an appendage with any desired trajectory to properly determine the stiffness of the flexors and extensors of an appendage. More particularly, a desired displacement of the wrist is first determined using a set of conditions detailed herein. A discrete set of finite points defining this trajectory is then input into a controller, and a motor shaft tracks these points at a certain sampling rate.
Other aspects and embodiments of the invention are discussed infra.